Question: Solve for $x$ and $y$ using elimination. ${5x-2y = 13}$ ${4x+6y = 18}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ ${15x-6y = 39}$ $4x+6y = 18$ Add the top and bottom equations together. $19x = 57$ $\dfrac{19x}{{19}} = \dfrac{57}{{19}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {5x-2y = 13}\thinspace$ to find $y$ ${5}{(3)}{ - 2y = 13}$ $15-2y = 13$ $15{-15} - 2y = 13{-15}$ $-2y = -2$ $\dfrac{-2y}{{-2}} = \dfrac{-2}{{-2}}$ ${y = 1}$ You can also plug ${x = 3}$ into $\thinspace {4x+6y = 18}\thinspace$ and get the same answer for $y$ : ${4}{(3)}{ + 6y = 18}$ ${y = 1}$